Periodic Anderson model is one of the most important models in the field of strongly correlated electrons.With the recent developed numerical method density matrix embedding theory,we study the ground state properties of the periodic Anderson model on a two-dimensional square lattice.We systematically investigate the phase diagram away from half filling.We find three different phases in this region,which are distinguished by the local moment and the spin-spin correlation functions.The phase transition between the two antiferromagnetic phases is of first order.It is the so-called Lifshitz transition accompanied by a reconstruction of the Fermi surface.As the filling is close to half filling,there is no difference between the two antiferromagnetic phases.From the results of the spin-spin correlation,we find that the Kondo singlet is formed even in the antiferromagnetic phase.